---
title: Sets & Operations
description: This topic covers the foundational concepts of set theory, including subsets, unions, intersections, and complements. Learners will understand how to manipulate sets using Venn diagrams, prove basic set identities, and apply set operations to solve logical and algebraic problems.
category: mathematics
subcategory: set-theory
difficulty: beginner, intermediate, advanced
url: /subject/sets-and-operations
---

# Sets & Operations

This topic covers the foundational concepts of set theory, including subsets, unions, intersections, and complements. Learners will understand how to manipulate sets using Venn diagrams, prove basic set identities, and apply set operations to solve logical and algebraic problems.

## Available Resources

1 Courses • 3 Websites

## Websites

### 1. Brilliant.org Sets

Community-written wiki page introducing sets, with notation, subsets, union, intersection, complement and cardinality, each followed by worked examples and short practice problems. Readers come away able to read set-builder notation and compute basic set operations and Venn diagram counts.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://brilliant.org/wiki/sets/

**Tags:** set notation, union and intersection, venn diagrams, cardinality

### 2. Wikipedia: Set Theory

Encyclopedia article surveying set theory as a branch of mathematical logic, from Cantor's work and the paradoxes to ZFC axioms, ordinals, cardinals and independence results. Readers get a map of the field's history, vocabulary and main research areas, with references.

**Difficulty:** Beginner | **Price:** Free

**Link:** https://en.wikipedia.org/wiki/Set_theory

**Tags:** set theory, zfc axioms, cardinal numbers, mathematical logic

### 3. Wolfram MathWorld

**Author:** Eric W. Weisstein

MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://mathworld.wolfram.com

**Tags:** mathematics-reference, encyclopedia, abstract-algebra, number-theory, geometry

## Courses

### 1. Introduction to Mathematical Thinking

**Author:** Keith Devlin

Stanford course by Keith Devlin on how mathematicians reason, starting with the logic of language (and, or, not, implication, quantifiers) and moving to the structure of proofs, including contradiction and induction. Learners become able to read, construct and critique simple mathematical proofs.

**Difficulty:** Beginner | **Language:** English | **Duration:** Expect to require at least 10 hours of study per week to complete this course satisfactorily. | **Price:** Free

**Link:** https://www.coursera.org/learn/mathematical-thinking

**Tags:** mathematical-logic, proof-writing, quantifiers, mathematical-reasoning

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